A molecular dynamics study proposing the existence of statistical structural heterogeneity due to chain orientation in the POPC-cholesterol bilayer

Journal Pre-proof A molecular dynamics study proposing the existence of statistical structural heterogeneity due to chain orientation in the POPC-cholesterol bilayer ´ ´ Fernando Favela-Rosales, Arturo Galvan-Hern andez, Jorge ´ Hernandez-Cobos, Naritaka Kobayashi, Mauricio D. ´ Ortega-Blake Carbajal-Tinoco, Seiichiro Nakabayashi, Ivan

PII:

S0301-4622(19)30304-7

DOI:

https://doi.org/10.1016/j.bpc.2019.106275

Reference:

BIOCHE 106275

To appear in: Received Date:

11 July 2019

Revised Date:

2 October 2019

Accepted Date:

21 October 2019

Please cite this article as: { doi: https://doi.org/ This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

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A Molecular Dynamics Study Proposing the Existence of Statistical Structural Heterogeneity due to Chain Orientation in the POPC-cholesterol bilayer

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Fernando Favela-Rosales1,2 , Arturo Galván-Hernández1, Jorge Hernández-Cobos3 , Naritaka Kobayashi4, Mauricio D. Carbajal-Tinoco1, Seiichiro Nakabayashi4, Iván Ortega-Blake3,*

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Departamento de Física, Centro de Investigación y de Estudios Avanzados, Av. IPN No. 2508, México, DF, 07360, México. Tecnológico Nacional de México, Campus Zacatecas Occidente, Ave. Tecnológico No. 2000, Col. Loma la Perla, Sombrerete, Zacatecas, 99102, México. 3 Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México Av. Universidad s/n Cuernavaca, Morelos, 62251, México. 4 Department of Chemistry, Faculty of Science, Saitama University, Shimo-Ohkubo 255, Sakura-Ku, Saitama City, 338-8570, Japan.

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*

Highlights

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Graphical abstract

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[email protected]

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● There is a non-monotonic behavior in several properties of the POPC- cholesterol bilayer along a T/cholesterol diagram. ● There is a lateral heterogeneity lasting tens of nanoseconds for the POPC-cholesterol bilayer thickness. ● This heterogeneity is not compositional but arises from coherent local ordering, without any concomitant cholesterol enrichment present. ● We relate our results to the different activity of polyenes in a proposed phase diagram of this mixture.

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ABSTRACT

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We performed molecular dynamics simulations of a lipid bilayer consisting of POPC and cholesterol at temperatures from 283 to 308 K and cholesterol concentrations from 0 to 50% mol/mol. The purpose of this study was to look for the existence of structural differences in the region delimited by these parameters and, in particular, in a region where coexistence of liquid disordered and liquid ordered phases has been proposed. Our interest in this range of concentration and temperature responds to the fact that polyene ionophore activity varies considerably along it. Two force fields, CHARMM36 and Slipids, were compared in order to determine the most suitable. Both force fields predict non-monotonic behaviors consistent with the existence of phase transitions. We found the presence of lateral structural heterogeneity, statistical in nature, in some of the bilayers occurring in this range of temperatures and sterol concentrations. This heterogeneity was produced by correlated ordering of the POPC tails and not due to cholesterol enrichment, and lasts for tens of nanoseconds. We relate these observations to the action of polyenes in these membranes.

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Keywords: Lipid bilayers, Molecular Dynamics simulations, cholesterol, membrane structure.

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1. INTRODUCTION

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Cell membrane physical properties play an important role in many biological processes (e.g., Escribá and Nicolson [1]). This is particularly true in regard to transport through the membrane by means of ionic channels or pores. These processes are affected by changes in membrane structure, thickness and even stiffness (e.g., [2,3] ). Also, different membrane phases can lead to differences in biological activity or, more generally, the non-random lateral organization of the different lipids in the membrane, resulting in the appearance of domains involved in cellular signaling and transmembrane traffic [4]. The biological cell membrane is a complex system comprising a multitude of lipidic species and the presence of many other molecules such as proteins. It is thus important to understand the physical chemistry of membranes; its complexity demands the use of simple bilayer models, where our understanding can be extended to describe molecular mechanisms.

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Perhaps the simplest relevant model for the biological cell membrane is the 1-palmitoyl-2-oleoyl-sn-glycero-3phosphocholine (POPC)-cholesterol bilayer, together with the 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) bilayer. Both have been extensively used for characterization of domains and phase transitions (e.g., [5–7]). The relevance of the POPC-cholesterol system can be seen, for instance, in how experimental results on the formation of polyene pores in simple POPC-sterol bilayers were extended to produce a polyene derivative with a differentiated action in animal systems [8]. Similarly, simple theoretical models have been widely used to obtain information on complex systems. Here we present a detailed Molecular Dynamics (MD) study, along a possible phase diagram (T/Chol), of a POPC-cholesterol bilayer. We are interested in analyzing the structural features at these conditions to extend the understanding of experimental results on how polyene ion channel forms. Works by de Almeida et al. [9], Thewalt and Bloom [10], and Halling et al. [11], have proposed a phase diagram for the POPC and cholesterol mixture. They advanced the existence of liquid disordered (ld), liquid 2

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disordered plus liquid ordered coexistence (ld + lo) and liquid ordered (lo) phases in a region covered by temperatures from 288 to 313 K and cholesterol concentration from 0 to 50% mol/mol using fluorescence and NMR studies. An electrophysiological study of membrane ion conductance induced by Nystatin, a polyene antibiotic, along this diagram also shows that it is larger in the purported mixed phase [12]. Even if the determination of phase diagrams is a matter of debate [5], the ld + lo coexistence is generally accepted for binary mixtures of cholesterol and phospholipids with saturated acyl chains, such as 1,2-dipalmitoyl-snglycero-3-phosphocholine (DPPC) or sphingomyelin. The existence of phase coexistence in bilayers formed from binary mixtures of cholesterol with phospholipids having one saturated and one unsaturated acyl chain is not totally accepted and has been contested [5,13]. On the other hand, the correlation shown between Nystatin induced conductance [12] and the presence of the distinct phases proposed by de Almeida et al. [9] supports the proposal of such phase diagram. This is important, given the proposal that membrane structure is the determining factor in the relative action of polyenes in membranes with cholesterol (mammal) or ergosterol (fungal) [14]. Hence we looked for structural features that varied along the (T/Chol) diagram that could explain Nystatin induced conductance results [12]. Ferreira et al. [13] performed (R-PDLF)NMR experiments on POPC-cholesterol systems at 300 K and different cholesterol concentrations. They concluded that if phase coexistence exists, it must correspond to lateral domains with sizes much smaller than 100 nm length.

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The present work addresses the possibility that structural differences in this membrane can arise. Thus, we looked into a molecular description through an MD study of the lateral organization of bilayers at different conditions. There is a previous MD study [15] of this system at 303.15 K and 33.3 % cholesterol in the purported mixed phase region. In this work a random distribution of both lipids with some clustering of the cholesterol molecules was found. We wanted to see if the same pattern occurs at other T/Chol conditions and if there are other features that could explain the difference in polyene ion induced conductance. The presence of nanodomains in a POPC-cholesterol mixture with a small proportion of sphingomyelin was not observed under Atomic Force Microscopy [16]. The profile of a POPC/sphingomyelin 1:1 and 20% cholesterol supported bilayer presents clear differences in height in regions about 50 nm in length, and this pattern gets blurred as the amount of sphingomyelin is reduced. However, their scans correspond to windows of 500 nm, so small domains (< 10 nm in length) will be difficult to observe. Furthermore, they show that, for a mixture of POPC, DOPC, sphingomyelin and cholesterol the size of the ld domains is drastically reduced as the DOPC/(DOPC+POPC) ratio diminishes. In a mixture of POPC, brain sphingomyelin and cholesterol, the heterogeneous structures are smoothed out when the amount of the latter is increased. Hence, we hypothesized that in a POPC-cholesterol system, domains could appear in some of the regions of the T/Chol diagram, but they would be small in size (radius < 10 nm) and with small differences in height. We performed MD simulations of POPC-cholesterol bilayers along the T/Chol diagram, from 0 to 50% mol/mol cholesterol concentration and from 283 to 308 K. There have been previous MD simulations of this system (e.g.,[13,15,17,18]), but not along this range of values. A limitation of the MD approach is the possibility of a particular force field being unable to determine subtle effects or yield artificial findings. Pluhackova et al. [19] and Drolle et al. [20] studied the performance of different force fields in the description of monolayers and bilayers of different lipids, including POPC. Pluhackova et al. [19] found that, when 3

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comparing united atom GROMOS54a7 [21], the all-atom force fields CHARMM36 [22], Slipids [23–25], and Lipid14 [26] force fields all satisfactorily described the overall structural characteristics of phospholipid bilayers, and that lipid diffusion and water permeability were well described by the all-atom force fields while cholesterol was better represented by Slipids. However, there were still some deficiencies reproducing different observables in all lipid force fields. Thus, we decided to consider two force fields in order to validate a general trend and establish with confidence whether MD can predict subtle changes in the bilayers here considered. We used the GROMACS [27] package and the Slipids [23] force field, which seemed the most reliable in both Pluhackova et al. [19] and Drolle et al. [20]. We also used the CHARMM36 [22] force field, which is widely used and has been found to better reproduce the structure of the phosphatidylcholine headgroup and glycerol backbone [28].

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In order to verify the MD predictions on membrane thickness we performed AFM topographic measurements on a POPC/Chol (7:3) supported lipid bilayer [29–31]. We used a liquid-environment frequency modulation AFM (FM-AFM) [32] with atomic resolution that has been developed [33,34] in the past decade. This technique has opened a new window into the study of atomic-scale biological systems with a piconewton-order loading force to the samples [35,36]. This technique allowed us to determine a membrane profile detailed enough to test the MD findings.

2.1 Materials

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2. MATERIALS AND METHODS

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POPC and cholesterol purchased from Avanti Polar Lipids (Alabaster, AL, USA). PBS was purchased from Sigma Aldrich (Toluca, México). The lipids in powder form and their stock solutions in chloroform were kept at −20 °C.

2.2 Liposome preparation

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Small unilamellar vesicles (SUV) of POPC/cholesterol mixtures were prepared by adding the appropriate amounts of stock solutions into a round bottom flask (4321A-5) from Pyrex, NY, USA. The solvent was evaporated using an EYELA evaporator Type N-N (TOKYO RIKAKIKAI CO. LTD.), in a two-step cycle consisting of 45 minutes at 400 mbar at 40°C and 45 minutes at 72 mbar at 40 °C to ensure solvent and water evaporation. Repressurization was done using 99 % pure nitrogen. The dried lipid films were rehydrated to a final concentration of 0.25mg/ml with ultrapure water and placed in an ultrasonication bath for 1 hour (AS ONE, VS-100III, Japan).

2.3 Supported Lipid Bilayers The liposomal suspension was either used the same day or one day after preparation, in which case the suspension was stored at 4°C. To prepare SLB, grade V-5 muscovite mica disks of 15 mm in diameter from ALLIANCE Biosystems, Japan (01878-MB) were used as substrate. The disks were glued with epoxy glue onto 4

a Teflon base. SLB were prepared using the vesicle fusion method [29–31] as follows. Liposome suspension was heated to 40°C prior to incubation, as well as 4 mM CaCl2 solution. 75 μl of CaCl2 were added to a freshly cleaved mica followed by 125 μl of liposome emulsion. The mica was placed inside a Nunclon cell culture dish from Thermo Scientific (153066) purchased from Sigma Aldrich (Toluca, México) to prevent evaporation. The cell culture dish with the mica and the emulsion was placed on a hotplate (AS ONE, DP-2S, Japan) at 40°C. The sample was washed four times. The first, second and third times the sample was washed with three volumes of 100 μl of ultrapure water. On the fourth occasion, the sample was washed with five volumes of 100 μl of PBS. The elapsed time between each wash was: 15 minutes prior to vesicle deposition for the first wash and 10 minutes between each of the last three. The sample was then left to cool down to room temperature (18°C) for 1 hour prior to AFM imaging.

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2.4 FM-AFM

2.5 Simulation protocols

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Frequency modulation AFM (FM-AFM) measurements were performed in a home-built FM-AFM system with an ultra-low noise optical beam deflection sensor [33,37,38]. A cantilever was oscillated at its resonance frequency with a phase-locked loop (PLL) circuit (OC4, SPECS). The PLL circuit was also used for keeping an oscillation amplitude of the cantilever at a constant value and detecting a frequency shift of the cantilever resonance frequency induced by a tip-sample interaction force. The tip-sample distance was regulated with a customized AFM controller (ARC2, Oxford Instruments). NCHAuD silicon cantilevers purchased from Nanoworld were used. Their nominal resonance frequency and spring constant were 150 kHz and 42 N/m, respectively.

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Simulations were done at three different temperatures (283, 298 and 308 K) and cholesterol concentrations (mol%) varied from 0 to 50% in steps of 5%. For each cholesterol concentration the total number of molecules in the bilayer was always 512 (256 per monolayer). Beside the previously described simulations, we performed another one with four times the size of the 30% cholesterol system at a temperature of 298 K. Other six simulations for experimental results comparison purposes were implemented: 0% at 293, 300 and 303 K; 15% at 300 K and 50% at 300 and 321 K. The initial configurations for the systems were built using the CHARMMGUI [39] utility. The number of molecules for all simulated systems are listed in Table 1. Table 1. Composition of the simulated lipid bilayers. a number of lipid molecules, b number of cholesterol molecules, c cholesterol concentration (mol%) and d number of water molecules. Lipid

a

Nl

b

c

d

POPC

512

0

0%

23943

POPC

486

26

5%

23986

NChol

CChol

Nw

5

460

52

10%

23569

POPC

436

76

15%

23331

POPC

410

102

20%

20972

POPC

384

128

25%

22327

POPC

358

154

30%

21183

POPC

1432

616

30%

84732

POPC

332

180

35%

POPC

308

204

POPC

282

230

POPC

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256

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POPC

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45%

21693

50%

20334

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All simulations were performed in the NPT ensemble using the GROMACS 4.6.7 package [27] for the Slipids simulation and GROMACS 5.0.7 for CHARMM36, which includes the force switch cutoff function required for this force field. We used rectangular simulation cells with periodic boundary conditions. Simulations were performed for 220 ns using the last 150 ns for analysis. It has been shown that 60 ns are enough for membrane equilibration initiating with random distribution [15].

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The TIP3P [40] water model was used to solvate the system in the Slipids simulations. We used the NoséHoover thermostat [41,42] at different temperatures with a relaxation time constant of 0.5 ps; water and lipids were each coupled separately to the heat bath. Pressure was kept constant at 1 bar using a semi-isotropic Parrinello-Rahman barostat [43] with a time constant of 10.0 ps. Equations of motion were integrated with the leapfrog algorithm using a timestep of 2 fs. Coordinates were generally written every 20 ps except for the analysis of the lateral heterogeneity of the membrane thickness in which case coordinates were written every 0.01 ps. Long-range electrostatic interactions were calculated using the PME method [44,45]. A real space cutoff of 1.2 nm with grid spacing of 0.16 nm in the reciprocal space was employed. Lennard-Jones potentials were cut off at 1.2 nm, with a dispersion correction applied to both energy and pressure. All covalent bonds in lipids were constrained using the LINCS algorithm [46,47], while water molecule bonds were constrained using the SETTLE algorithm [48]. Twin-range cutoffs, 1.0 nm and 1.6 nm, were used for constructing the neighbor lists with the long-range neighbor list being updated every 10 steps. 6

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In the CHARMM36 simulations, the CHARMM TIP3P [49] water model was used to solvate the system. We employed the publicly available port of the CHARMM36 [22] forcefield parameters at mackerell.umaryland.edu/CHARMM_ff_params.html for both POPC and cholesterol. We used a timestep of 2 fs with the leapfrog integrator. All covalent bonds with hydrogen atoms were constrained with the LINCS [46,47] algorithm. Long-range electrostatic interactions were also calculated using the PME method [44,45] with real space cut-off of 1.2 nm. The neighbors lists with a cut-off of 1.2 nm were updated every 20 steps. We employed the force switch cutoff function required by this force field and recommended by the GROMACS website at www.gromacs.org/Documentation/Terminology/Force_Fields/CHARMM. Temperature was coupled separately for cholesterol, lipids and water, using the Nosé-Hoover thermostat with coupling constant of 1.0 ps. Pressure was semi-isotropically coupled to a pressure of one atmosphere with the Parrinello Rahman method using a time constant of 5.0 ps. Coordinates were written every 20 ps.

2.6.1 Area per lipid (POPC or cholesterol)

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2.6 Analysis

2𝐴(𝑥) (1−𝑥)𝑁𝑙𝑖𝑝𝑖𝑑

[1 −

𝑥𝑁𝑙𝑖𝑝𝑖𝑑 𝑉𝐶ℎ𝑜𝑙 𝑉(𝑥)−𝑁𝑊 𝑉𝑊

]

(1)

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𝐴𝑃𝑂𝑃𝐶 =

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The area per POPC (APOPC ) was calculated for each system in Table 1 according to the following formula [50]:

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where x is the cholesterol concentration, A(x) and V(x) are the area and volume of the simulation box respectively, Nlipid is the total number of lipids (512), Vchol is the volume of one cholesterol molecule [50] (0.593 nm3), Nw is the number of waters in the system and Vw is the volume of one molecule of water [50] (0.0312 nm3). The area per cholesterol Achol was calculated as the difference between the membrane patch area minus NPOPC × APOPC divided by the number of cholesterol molecules Nchol.

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2.6.2 Order parameters

The LOOS [51] tool order_params was employed to calculate the order parameters. The order parameters are defined as follows: 1

𝑆𝐶𝐻 = ⟨3𝐶𝑜𝑠 2 𝜃 − 1⟩ 2

(2)

where θ is the angle between the membrane normal and the vector connecting the Carbon (C) atom to its hydrogen (H) atom(s), and ⟨⟩ represents the ensemble average. 7

2.6.3 Radial distribution functions and coordination numbers

𝑟2

𝐶𝑁(𝑟1 : 𝑟2 ) = ∫ 2𝜋𝑟 𝑔(𝑟)𝑑𝑟

(3)

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The radial distribution function (rdf) describes how the density of molecules varies as a function of distance from a reference particle and the coordination number yields an estimate of the number of molecules within a specific range of distances from this same reference particle. For the 2D radial distribution function and coordination numbers we used the GROMACS tool g_rdf [27] using the projected center of mass positions of the lipid molecules, this was done for each monolayer and then averaged between them. The number of neighboring molecules in the vicinity (coordination number) between two radial distances was obtained using the formula:

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Lipid-lipid radial distribution functions for particular regions of the membrane were obtained by selecting molecules present in these regions and computing the radial distribution functions centered on them with the rest of the molecules in the system. This was done with an in-house program.

2.6.4 Membrane thickness

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The thickness of the bilayer was determined by measuring the distance between maxima of the headgroups electron density obtained using the GROMACS tool g_density [27]. The headgroup components are: choline methyl, phosphate + CH2CH2N and carbonyl + glycerol [52]. This procedure was employed when the membrane thickness was considered as an average value of the whole patch.

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To characterize the lateral heterogeneity in the systems, membrane thickness was also computed as short time averages in small regions. A grid of 9x9 squares was constructed for each simulation cell. In each element of the grid, the membrane thickness was computed as follows. First an average electron density profile was constructed with 5 snapshots separated by 20 ps. A thickness was calculated from this profile. In this case, electron density peaks were not well defined, so the thickness was computed as the distance between the points at which the electron density reached 50% of the peak value predicted for the whole bilayer patch (168 electrons/ nm2). Then, 0.6 nm were subtracted to make this estimation comparable with the peak-peak thickness calculated with g_density [27]. This process was performed all along the time period considered and an average of the thickness values was obtained. Local membrane thickness values are shown without any form of interpolation to prevent result distortion, even if the picture appears pixelated. Each pixel corresponds to one of the 81 boxes in which the membrane patch was partitioned. The 9x9 grids were used to calculate the thickness weighted pair distribution function: 𝐺ℎℎ (𝑟) =

⟨h(𝑥⃗) × h(𝑥⃗ + 𝑟⃗)⟩ − ⟨h(𝑥⃗)⟩⟨h(𝑥⃗ + 𝑟⃗)⟩ 𝜎2

(4)

where 𝑥⃗ is any specific point in the image and 𝑟⃗ is a displacement vector, brackets denote an ensemble average 8

over the radial distance 𝑟, and 𝜎 is the standard deviation of the whole collection of values. This was done with an in-house program. The autocorrelation functions were calculated using the autocorr function of matlab using time gaps up to half the length of the sample.

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The previous procedures were applied to the simulation of the large patch (2048 lipids) but now a 18x18 grid was used. A thickness line profile was constructed in the large membrane patch. We computed the average value and the corresponding standard deviation by dividing the time considered in 3 blocks.

2.6.5 Figures

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Figures were generated with gnuplot [53], Grace [54] and matlab [55]. Contour plots were produced using the contour function of gnuplot with the following interpolation parameters: bspline, order 5 and levels 30. The lateral distribution of thickness (Figures 8 and 13) was generated using the imagesc function of matlab. The cholesterol positions were drawn with gnuplot.

3.1 Global properties Area per lipid

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3. RESULTS

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APOPC for a fully hydrated POPC bilayer (0% cholesterol) predicted by numerical simulations at different temperatures with both force fields are presented in table S1. The results show that both force fields produce values close to the experiment and, as reported before [24], Slipids is slightly above the experimental values. Other values commonly used for parameterization are the order parameters measured by NMR. Figure S1 shows the order parameters for the different carbons in the palmitoyl and oleoyl chains predicted by the two force fields and compares them to the experimental results of Ferreira T.M. et al. [13]. There is a general agreement between both force fields and the experimental results, even if both tend to overestimate order. There are, however, differences. Slipids predicts values closer to the experimental ones, mainly for carbon 10 in the sn2 tail. CHARMM36 predicts two values for carbon 2 of sn2 that are close to the experimental ones. Slipids yields a smaller difference between these two values, making them appear closer to the more ordered experimental point. The previous results show that both force fields are able to reproduce experimental characteristics or the POPC membrane. We can then look into the predicted values of APOPC for different conditions of temperature and concentration. We still use both force fields in order to compare their performance. An experimental determination by 13C NMR of the area per lipid (POPC and cholesterol) of a membrane of POPC-cholesterol 9

50% yields a value of 0.451 (0.009) nm2 at 321 K [56]. The area per lipid for POPC-cholesterol 50% at 321 K predicted by our calculations is 0.423 (0.004) for Slipids and 0.427 (0.001) for CHARMM36. These two amounts are smaller than the experimental counterpart, indicating that a more packed structure is predicted. This may be due to the fact that both force fields overestimate order, as stated above.

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Figure 1 shows APOPC for different concentrations and temperatures. This property is more dependent on cholesterol concentration than on temperature, and has a monotonic dependence up to concentrations ~35%. At these concentrations there is an inversion on the slopes of the contour lines. This singularity occurs close to one of the transition lines proposed by de Almeida et al. [9] In Figure 2, the APOPC as a function of cholesterol shows a slight reduction of the expected packing at high cholesterol, suggesting a crystal like formation demanding more space resulting from some form of cholesterol networking. This is corroborated in the twodimensional radial distribution function cholesterol-cholesterol at 50% cholesterol and T = 298 K shown in Figure 3. We computed the cholesterol-cholesterol radial distribution function for other conditions and in all cases it showed considerable structure, like that of a very ordered liquid. All these findings are very similar for both force fields. The dependence of AChol on temperature and cholesterol concentration is presented in table S2.

Figure 1. APOPC in nm2 predicted by the different force fields along the T/Chol diagram. The black dots and broken lines correspond to those of de Almeida et al. [9] that define the purported ld/(ld + lo) and (ld + lo)/lo transition lines.

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Figure 2. APOPC in nm2 as a function of cholesterol concentration predicted by the two force fields. The shaded area corresponds to the associated error.

Figure 3. 2D radial distribution function between center of mass positions of cholesterol-cholesterol and the corresponding coordination number. For a 50% cholesterol membrane at T = 298 K. Slipids in black and CHARMM36 in red.

Membrane thickness One parameter that could reflect structural differences produced by a different order is membrane thickness. 11

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Figure 4 shows this property as predicted by both force fields along the T/Chol diagram. Slipids predicted a ~3.75 nm thickness in the ld region with a variation of less than 5%, while thickness in the lo region was ~4.3 nm with a variation of less than 3%. These values are close to the 4.00 nm obtained for a multilamellar arrangement by Leftin et al. [56] using NMR. On the other hand, in the region of the (ld + lo) mixture, membrane thickness shows a variety of values (from 3.75 to 4.3 nm) with a considerable dependence on temperature. CHARMM36 provides a similar pattern but a more ordered membrane for large cholesterol concentrations. This behavior was also observed by Olsen et al. [18] using the Berger force field [57]. The fact that membrane thickness changes considerably along the T/Chol diagram may be due to the orientation of lipid chains with respect to the membrane normal. This was also reported by Ferreira T.M. et al. [13], who presented the projected length in the bilayer normal of the sn1 chain as determined by both MD and NMR. They considered cholesterol concentrations from 0 to 50% mol/mol at 300 K and obtained a variation very similar to ours, ~25%. Our results show that temperature dependence is only present in the purported coexistence phase region. The lo region has an almost constant thickness that could be due to an almost complete tail orientation to the membrane normal.

Figure 4. Membrane thickness. The black dots and broken lines correspond to those of de Almeida et al. [9] and define their purported ld/(ld + lo) and (ld + lo)/lo transition lines.

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There is an experimental determination by small-angle X-ray diffraction of membrane thickness variation for a POPC membrane with cholesterol concentration ranging from 0 to 20% mol/mol [58]. A transition phase is also observed at 5% and with temperature independence from 283 to 323 K. This differs from the transition reported by de Almeida et al. [9] at 10% and with a very slight dependence on temperature. In their research, membrane thickness was slightly dependent on cholesterol concentration. The difference between both experimental determinations and, generally speaking, with respect to phase diagrams [5], prevents us from properly contrasting our predictions.

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Order

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Variations in membrane thickness along the diagram are due to changes in the orientation of the POPC molecules with respect to the membrane normal. It is therefore possible that the order parameter of the POPC tails have marked differences along it. Figures 5 and 6 show the average order parameters of carbon C2 for the two tails.

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Figure 5. Average order parameter of carbon C2 of the palmitoyl chain predicted by both force fields along the T/Chol diagram. Slipids (left) and CHARMM36 (right).

Figure 6. Average order parameter of carbon C2 of the oleoyl chain predicted by both force fields along the T/Chol diagram. Slipids (left) and CHARMM36 (right). Figures 5 and 6 show that the contour map for the palmitoyl chain is very similar for both force fields, whereas there are substantial differences for the oleoyl chain. CHARMM36 predicted a less ordered oleyl chain for the 13

whole diagram. Both force fields show a slightly non-monotonic behavior for both chains, mainly in the purported mixed phase region. It should also be noted that the saturated palmitoyl chain is highly ordered, whereas the unsaturated oleoyl chain is not. Both force fields are able to detect structural changes in the membranes of the POPC-cholesterol mixtures at different temperatures. This shows that MD simulations have the ability to reproduce structural changes. The force fields comparison indicates that Slipids is slightly closer to experimental values, so we decided to delve into membrane molecular properties using this force field only.

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We also looked into each region’s structure by computing the 2D lipid-lipid radial distribution function at different cholesterol concentrations. Figure 7 shows how increasing cholesterol leads to a more structured pattern. The corresponding coordination numbers are also shown in Figure 7 and Table 2. The first closest neighbor values converge to 5 as cholesterol concentration increases; the second converge to a value of 8. These values are in agreement with a distorted hexagonal arrangement, an orthorhombic one that is characteristic of the gel phases of some lipid structures.

Figure 7. 2D lipid-lipid radial distribution functions of membrane patches of POPC-cholesterol at 298 K and the corresponding coordination numbers predicted by the Slipids force field for different cholesterol concentrations.

Table 2. Properties of the different coordination shells for Chol-Chol and lipid-lipid radial distribution functions at 298 K predicted by the Slipids force field. Peak distance, minimum distance, and coordination number (CN). 14

1st Shell

2nd Shell

3rd Shell

Chol-Chol rpeak

rmin

CN

rpeak

rmin

% Chol

(nm)

(nm)

50

0.62

0.88

rpeak

rmin

(nm)

(nm)

5

0.84

1.28

7.5

30

0.72

0.96

5.3

1.10

1.37

45

0.65

0.91

5.2

1.08

1.38

CN

(nm)

(nm)

2.4

1.07

1.36

3.9

CN

rpeak

rmin

CN

rpeak

rmin

(nm)

(nm)

1.57

1.8

CN

5.2

3.2 Local properties

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rmin

CN

(nm)

(nm)

6.4

1.56

1.89

11.3

8.0

1.57

1.86

11.6

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(nm)

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lipid-lipid

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All the quantities considered up to now are averages on the total time of the simulation and on the whole membrane patch. The dispersion of values encountered suggests there could be local variations of these properties. Local variations of structural properties of the membrane can have an effect on molecular processes occurring in them, even if they last for a short time (i.e. ns). Furthermore, recalling the concept of statistical geometry [59], we could also expect that such local variations could be of statistical nature, as in the liquid state. In order to assess this, we considered the lateral distribution of the membrane thickness of the patches at different temperatures and cholesterol concentrations. Previous studies looking into membrane local properties of the POPC-sphingomyelin-cholesterol system [60] found a correlation between order parameter and membrane thickness, as well as the fact that both cholesterol and sphingomyelin induce order in membrane domains. A recent study of a DPPC–cholesterol membrane, using coarse grained simulations [7], found that several local properties showed heterogeneous distribution. As mentioned by Niemelä et al. [60], time averages of local properties can vary substantially if there is considerable molecular motion in the membrane. Given the diffusion rate of lipids in a membrane, we can expect that molecules barely move in a period of 150 ns. That said, chain movement is much faster and, thus, membrane thickness could change considerably due to this motion. We decided to compute the lateral distribution of the membrane thickness along the T/Chol diagram. This is shown in Figure 8, where clear 15

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differences can be observed. It should be mentioned that this behavior is not reproduced in every single snapshot, but is the result of statistical averaging, identical to the statistical geometry behind liquid structure [59]. Figure 9 shows examples of lateral views of membranes for low Chol concentration and high temperature, medium Chol concentration and temperature and high Chol concentration and low temperature, highlighting the differences that these parameters produce in the membrane order.

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Figure 8. Lateral distribution of membrane thickness (nm) for POPC-cholesterol patches at different temperatures and cholesterol concentrations predicted by the Slipids force field.

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Figure 9. Lateral views of POPC-cholesterol membranes snapshots, produced by SLIPIDS after 150ns. POPC tails are in magenta, phosphates in orange, choline in green, cholesterol in cyan and the cholesterol oxygen in red. The number of lipid molecules is the same for all cases, but packing as cholesterol concentration increases reduces the membrane lateral dimension and increases membrane thickness.

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Figure 8 shows the expected effect of cholesterol in ordering the membrane, as well as the disordering effect of temperature. At 5% cholesterol there is little effect of temperature, in agreement with Figure 4, and also quite a homogeneous distribution. At large cholesterol concentration (50%), Figure 4 shows a small effect from temperature. This is not so clear in Figure 8, but if we compute the average value for thickness in the whole patch, values of 4.36, 4.42 and 4.47 nm are obtained for 305, 298 and 383 K respectively, which are in agreement with those in Figure 4. It is interesting to note that a distinguishable pattern along the T/Chol diagram appeared, which we did not interpolate to avoid distortion of the findings. There is a statistical heterogeneity, characterized by small regions with similar values of thickness surrounded by regions of different thickness. This heterogeneity seems to be more marked in the intermediate columns. Even more so, the largest local values for thickness, and therefore the more ordered membrane, do not occur at the largest cholesterol concentration, but in regions of medium cholesterol concentration and low temperature. We have to remember that these values are averages over 150 ns, a very long period compared to the orientational motion of cholesterol and lipid tails. Hence it seems that there is a local orientational correlation in the membrane. The 17

fact that we can observe this in a period of 150 ns suggests that this correlation could be more marked in shorter periods. Thus, we looked into the height lateral distribution for shorter periods. In these cases, the differences in height were more marked, but the regions were more loosely defined. This will be discussed further ahead in detail when a larger membrane patch is presented.

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To check the statistical significance of these findings, we computed the thickness weighted pair distribution functions (Ghh) that have been used to determine the existence of domains [61]. Results for Ghh in patches along the T/Chol diagram for periods of 150 ns show evidence of nanodomain presence, indicated by positive values extending up to ~3-4 nm, where anticorrelation, negative values, arises. This is shown in Figure S3. At high temperature and large cholesterol concentration, no appreciable domain formation can be observed at all. This latter result is in agreement with Atomic Force Microscopy [16] findings. Correlation/anticorrelation profile is more marked at 20% cholesterol and a temperature of 283 K in the mixed phase region. Another issue is the persistence time of nanodomains in the membrane surface, which can be determined from the time autocorrelation function of the membrane thickness presented in Figure S3. The temperature effect is only noticeable for the 5% cholesterol column and cholesterol concentration does not seem to affect the time correlation profile. Summarizing, persistence is short and hardly affected by temperature or cholesterol concentration.

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Large Membrane

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Our results can be affected by the size of the membrane patch. Hence, we performed a simulation with a 4-fold increase in area. Figure 10 presents the local thickness distribution corresponding to a POPC membrane with 30% cholesterol at 298 K. We present averages over subsequent periods of 30 ns, covering the 150 ns simulation, in order to look into the evolution of the thickness profiles and, thus, of the lateral statistical heterogeneity. The evolution of patterns along the different panels shows some persistence of this heterogeneity, but also the shifting of the regions within this time scale. This can be understood as the result of averaging white noise in the thickness values for the different squares in the grid, and the appearance of defined regions for averages of long enough time periods. These periods must be limited because of the shifting of the nanodomains in time. This heterogeneity is quite distinct from that arising from domains with different composition: In our case, it is statistical in nature and could entail important molecular processes within its dimensions and life time. We can estimate these two values from thickness correlation as a function of distance (Figure 11a) and time (Figure 11b). Figure 11a shows a complete oscillation of Ghh, predicting the presence of correlated thickness in a ~4 nm radius domain and Figure 11b shows the time persistence of these nanodomains. Since membrane ordering and thickening is affected by cholesterol concentration, the patterns observed could be the result of varying cholesterol distributions. Hence, we looked into the cholesterol distribution presented in Figure 10. We present the cholesterol positions of the last snapshot of one leaflet of the membranes. We used only one leaflet to better observe cholesterol density, avoiding overlapping of cholesterol molecules from both layers. As can be seen, there is a lack of correlation between cholesterol distribution and high or low thickness regions. There is no cholesterol enrichment of the regions where more order appears, as might be expected. 18

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Figure 10. Lateral distribution of membrane thickness (nm) for a POPC-cholesterol membrane patch of 482.52 nm2. Computed with Slipids force field in subsequent averages of 30 ns. The patch has 30% cholesterol concentration and a temperature of 298 K. In the figures the last snapshot of the cholesterol positions of a leaflet are presented as red dots. Regions highlighted in the first panel were used to calculate the rdf shown in Figure 12 for high and low order regions.

(a)

(b)

Figure 11. (a) Thickness correlation as a function of distance and (b) thickness autocorrelation as a function of time for a 482.5 nm2 patch having POPC and 30 % cholesterol at 298 K. Results obtained with the Slipids force field.

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A very precise determination of the local structure of a liquid is the lipid-lipid radial distribution function. A very strong confirmation of the existence of the purported local domains would be to observe differences in the the rdf centered on lipid molecules belonging to different domains. In Figure 12 we present these functions corresponding to the low and high thickness regions indicated in the first panel of Fig. 10. As can be seen, the low thickness regions have a rdf with a local density lower than the bulk values and a very faint order profile, except for the first peak. On the other hand, the high thickness regions have a rdf with a more defined local order profile and certainly higher density than the bulk. Hence, these results support the proposal of the existence of statistical heterogeneity in the membrane.

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Figure 12. Averaged lipid-lipid radial distribution functions of the regions indicated in the first panel of Figure 10 corresponding to a 482.5 nm2 patch having POPC and 30 % cholesterol at 298 K simulated with the Slipids force field. The red line corresponds to the average of the low thickness regions and the black line to the average of the high thickness regions.

Experimental evidence of the occurrence of thickness variation of a lipid bilayer has been given by means of AFM studies, for instance Ho et al. [16]. We wonder if a statistical geometry pattern could be observed in these cases, obviously with a totally different time scale. Hence, using high resolution Frequency Modulation Atomic Force Microscopy, we performed topographic images of the surface of a supported lipid bilayer of POPC/Chol (9:1 mol/mol). In Figure 13a we present the average of 20-line profiles ~1 nm apart, yielding a similar width to the simulation patch. This line profile shows thickness variations greater than the noise present in the curve. This structure, of statistical origin, should result in a Ghh(r) showing the existence of regions with correlated and 20

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anticorrelated height. In Figure 13b we present Ghh(r) obtained from the topographic image of a 250x250 nm2 patch of the same bilayer. We can see a correlation-anticorrelation profile characteristic of an inhomogeneous surface, of course occurring in a large time scale. A complete FM-AFM scan takes approximately 30 s.

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Figure 13. FM-AFM determination of thickness of a supported lipid bilayer of POPC and 10 mol% cholesterol at 18°C (a) Height profile obtained averaging 20 scan lines one nm apart. (b) Height-height correlation function for a 250x250 nm2 patch of the same system.

4. DISCUSSION

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The comparison of the properties predicted by the two force fields gives confidence on the numerical simulation results with respect to force field dependency, since they are similar. The area per lipid, the membrane thickness and the order parameter of the C2 of both POPC tails clearly show a non-monotonic behavior along the T/Chol diagram. The correlation between the non-monotonic regions’ occurrence with the transition lines proposed by de Almeida et al. [9] suggest the existence of the purported phase diagram. A detailed analysis of the molecular behavior occurring in the simulations at different points of the T/Chol diagram shows that there is some form of heterogeneity of the membrane structure in this binary mixture. We found that a statistical heterogeneity could be observed when local thickness was determined. Thickness presents considerable fluctuations both in time and space, so snapshots do not present a clearly defined 21

heterogeneity. On the other hand, if one considers statistical averages, the structural heterogeneity is clearly apparent. The relevance of this phenomena is that it can affect molecular processes due to the scale of its persistence in space, several nanometers and tens of nanoseconds. The statistical nature of this phenomena is similar to the one present in the structure of liquids [59], which has proved to be very important. We found that this heterogeneity seems to arise from correlated POPC tail ordering. We corroborated the existence of this heterogeneity by computing the local lipid-lipid 2D radial distribution function in the purported regions of different thickness. It was found that the higher thickness regions presented a radial distribution function corresponding to a more ordered liquid. The low thickness regions presented a radial distribution function corresponding to a less ordered liquid and low local density compared to the bulk, suggesting loose packing.

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This heterogeneity varied considerably along the T/Chol diagram. At low cholesterol concentration it is only present at low temperatures and, at large concentrations, it appears quite fractured. This dependence on concentration resembles that found for compositional domains. It is interesting that in the purported region of the mixed phase heterogeneity is better defined, with more contrast and larger aggregates. To our surprise cholesterol depletion or aggregation was not the reason for the purported heterogeneity. This is not compositional in nature but surges from a correlation of tails orientation within tens of nanoseconds.

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It is worth noting that cholesterol aggregates in the phospholipid matrix appear in single file arrangements at large cholesterol concentrations. This clustering could explain the non-linear response to sterol concentration (see Figure 8). This non-linear response to sterol concentration has been previously reported for model membranes and even in cells. For instance, the experimental finding that an increase of the ergosterol fraction in the membranes of fungal cells can lead to their resistance to the pore forming antimycotic polyene Amphotericin B [62,63]. Another non-linear behavior is proposed by the crystallite model —that there is a gradual effect with increasing sterol membrane fraction until saturation is reached. At this point a phase separation of sterols in the membrane takes place; for a review see Bach and Wachtel [64].

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In a study of the DPPC-cholesterol mixture by coarse grained Molecular Dynamics, Wang et al. [7] fail to observe local domains in the membrane thickness. This is surprising since the presence of a mixed phase is well accepted in this system. However, we have to mention that in some of their membrane thickness diagrams, for instance at 350 K and 10% cholesterol well into the pure lo phase, there are some profiles similar to ours, even if not as well defined —possibly due to averaging local values for up to 100 ns. The idea that local heterogeneity is statistical in nature is supported by the results of the thickness correlation functions and the autocorrelation functions. We also consider the effect of the simulation box size on the characteristics of thickness heterogeneity. Results in a large patch show again regions of lateral statistical heterogeneity, better defined and having similar sizes than those in the smaller patches. In the case of binary mixtures of phospholipid and cholesterol, cholesterol heterogeneity should appear as clustering in the phospholipid matrix. The lateral inhomogeneity of cholesterol in such membranes has been recently addressed [65]. The conclusion, based on coarse grained simulations of cholesterol and unsaturated lipids performed with the Martini force field was that lateral cholesterol organization is dominated by weak repulsive forces and a homogeneous distribution should therefore be expected. Our results, with an atomistic force field, yield precisely this, but with slight cholesterol clustering of two to five molecules. A similar finding was reported by Hong et al. [15] for the POPC-cholesterol mixture at 30 % cholesterol. The single file 22

arrangements found by us become more apparent at larger concentrations of cholesterol and agree with the cholesterol-cholesterol radial distribution functions. However, we did not find very large clusters > 5, as those reported in the work of Bennet et al. [66]. Of course, in our case we have a lipid with both saturated and unsaturated tails.

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It has been proposed that in ternary mixtures of cholesterol with saturated and unsaturated lipids there is separation of the different phospholipids and a concomitant cholesterol enrichment driven by a more favorable enthalpy in saturated lipids domains [67–70]. However, in a recent atomistic long-timescale simulation of a mixture of 1,2-distearoyl-sn-glycero-3-phosphocholine, 1,2-dilinoleoyl-sn-glycero-3-phosphocholine, and cholesterol [66] there is a disagreement with the above prediction. Domain formation is directly observed, but no cholesterol enrichment on the saturated lipid domain. Actually, the cholesterol distribution is not homogeneous. Clustering of cholesterol appears at the interphase of the domains, even if some cholesterol molecules also appear within the domains themselves, mainly in the saturated ones. These new results are in agreement with the experimental results of Fisz et al. [71], who found no cholesterol enrichment in the ordered sphingomyelin domains.

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5. CONCLUSIONS

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As in the case of Pluhackova et al. [19] and Botan et al. [28], we found general agreement between the predictions of different force fields. The force fields employed, Slipids and CHARMM36, have shown interesting overall changes of several observables to which experimental techniques are sensible.

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Molecular properties of membranes such as area per lipid, membrane thickness and order parameters show a non-monotonic behavior along the T/Chol diagram. The results emphasize the complex dependency of lipid membrane structure on temperature and composition.

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We found a local heterogeneity, albeit statistical in nature, better defined at 283 K and 20-30% Chol concentration. The existence of different regions leads to differences in the lipid-lipid radial distribution functions and local density in the membrane. This heterogeneity leads to the existence of borders where average membrane thickness changes suddenly.

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Domain borders could facilitate the insertion of the polyene into the membrane [12]. In a recent work [72], this idea is further supported by showing a greater channel activity of Nystatin in the presence of highly ordered domains in a POPC-sphingomyelin and POPC-DPPC mixtures. This idea would be strongly supported if ergosterol proved more effective than cholesterol in producing local statistical heterogeneity and, thus, marked borders. Such a study is under way.

Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 23

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

ACKNOWLEDGEMENTS

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The authors acknowledge: César Millán for useful discussions; Reyes García for technical support; ITSZO, CONACYT Grant 152532, DGAPA- PAPIIT-IG100416 and the "Takeda Science Foundation" for financial support; Clúster Híbrido de Supercómputo Xiuhcoatl-CINVESTAV and Miztli-UNAM for computational resources.

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The Supporting Material shows in table S1 the Area per POPC in sterol free membranes at different temperatures predicted by both force fields and compared to experiment. In table S2 the area per cholesterol predicted by both force fields, at different temperatures and cholesterol concentrations, is presented. In figure S1 the order parameters of the POPC acyl chains predicted by both force fields, for different cholesterol concentrations at 300 K, is presented. In figure S2 the thickness correlation functions for different temperatures and cholesterol concentration, predicted by the Slipids force field, are presented. In figure S4 the thickness autocorrelation functions for different temperatures and cholesterol concentration, predicted by the Slipids force field, are presented.

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